Hi there - my grandfather is also William Douglas Deavers. My father, John Henry Deavers, is one of his children by his first wife, Shirley Nachiste, and a namesake for our great grandfather. I had always wondered if William Douglas remarried - I guess that's makes you a half cousin or some such!
I don't have a ton of information, I'm looking as well, but I do know John Henry's parents were John M. Deavers b.1842 and Amanda Jane Parker b. 1848.
The children from JH's first marriage to Susan Bennett were Minnie Lee, Winnie Lee, Miles Ray and Mary Augustus.
Hope that helps! If you have any other info, my email address is firstname.lastname@example.org